The McKay-Navarro Conjecture: the Conjecture That Keeps on Giving!

Abstract: The McKay conjecture is one of the main open conjectures in the realm of the local-global philosophy in character theory. It posits a bijection between the set of irreducible characters of a group with $p'$-degree and the corresponding set in the normalizer of a Sylow p-subgroup. In this talk, I’ll give an overview of a refinement of the McKay conjecture due to Gabriel Navarro, which brings the action of Galois automorphisms into the picture. A lot of recent work has been done on this conjecture, but possibly even more interesting is the amount of information it yields about the character table of a finite group. I’ll discuss some recent results on the McKay—Navarro conjecture, as well as some of the implications the conjecture has had for other interesting character-theoretic problems.

group theory

Audience: researchers in the topic

Finite Groups in Valencia

Series comments: The seminar meets weekly from February 26th to March 30th 2021.

For a detailed schedule and registration details, please visit the seminar webpage at

sites.google.com/view/finite-groups-seminar2021